The majority of theoretical misconceptions and the most significant misunderstandings in modern astronomy, cosmology and physics are caused by a purely mathematical approach and ignoring philosophical comprehension of physical reality and, as a result, by not deep enough understanding of the essence of certain physical phenomena and objects.

The cardinal difference between relativistic gravithermodynamics (RGTD) and general relativity (GR) is that in RGTD the extranuclear thermodynamic characteristics of matter are used in the tensor of energy-momentum to describe only its quasi-equilibrium motion.

Термодинамічна інтерпретація загальної теорії відносності та розглядання Всесвіту як єдиного спіральнохвильвого утворення, а так званих елементарних частинок і кварків як кінцевих локальних стоків цих спіральних хвиль фактично дозволили створити «теорію всього»

Thermodynamical interpretation of General Relativity, consideration of the Universe as a single spiral-wave formation, and consideration of the so-called elementary particles and quarks as finite local flows of these spiral waves actually allowed the creation of a "theory of everything".

The equations that combine the instantaneous values of main thermodynamic parameters and potentials (that are characteristic to Gibbs thermodynamic microstates) of the simplest gases and liquids were found.

The quantum equation of gravitational field have been found, the solutions of which set the spatial distribution of gravitational radius of matter in its every new gravithermodynamic (GTD) state with the polynomial function with the next more high degree.

Only conditional identity of inertial mass of moving matter to its gravitational mass only by gravity-quantum clock, which is located in the point, from which the matter started its inertial motion, and due to the usage of corrected value of gravitational constant in its pseudo-centric intrinsic frame of reference of spatial coordinates and time (FR), is justified.

Кардинальное отличие релятивистской гравитермодинамики от общей теории относительности заключается в использовании в тензоре энергии-импульса внеядерных термодинамических характеристик вещества для описания лишь его квазиравновесного движения.

The general solution of the equations of the gravitational field of the galaxy with an additional variable parameter n is found. The additional variable parameter n determines in GR the distribution of the average mass density mainly in the friable galactic nucleus

It is shown that, according to the General Relativity, only the transverse metric distances – the transverse comoving distance and the angular diameter distance similar to it – can obey the Hubble linear dependence. The transverse comoving distance belongs to the comoving reference of spatial coordinates and time in the expanding Universe and is determined by the redshift of the emission wavelength.

The equivalence of only inert free energy of matter (and not of the total internal energy) to gravitational and inert masses is justified. It was proved that total energy of matter of inertially moving body is equal in all frames of references of spatial coordinates and time that are moving relatively to matter. And that is precisely why there is a conform Lorentz-invariance of thermodynamic potentials and parameters in examined modification of transformations of the special theory of relativity

It was shown that Etherington’s identity is paralogism. Etherington’s identity is based on the imaginary relativistic dilation of intrinsic time of the galaxy by (1+z) times, but the presence of a relativistic anisotropy of luminosity of stars quickly moving away from it is ignored in the frame of reference of spatial coordinates and time of the observer.

The most perfect modification of the special and general theories of relativity is considered. It is shown that equations of the gravitational field of General Relativity (GR) should be considered as equations of spatially inhomogeneous gravithermodynamic state of only utterly cooled down matter. This matter can only be the hypothetical substances such as ideal gas, ideal liquid and the matter of absolutely solid body. The real matter will be inevitably cooling down for infinite time and never will reach the state that is described by the equations of gravitational field of the GR.

Основна мета цього дослідження – виявлення наукових оман і найбільш значних непорозумінь в сучасній астрономії, космології і фізиці. Більшість з них викликано як суто математичним підходом, так і ігноруванням філософського осмислення фізичної реальності. І як наслідок цього, – недостатньо глибоким розумінням сутності деяких фізичних явищ і об'єктів. І, перш за все, це стосується явищ і об'єктів, що розглядаються в спеціальній і загальній теоріях відносності.